Millimeter Wave Absorption in Superconducting Aluminum. I. Temperature Dependence of the Energy Gap

Measurements of the temperature dependence of the microwave absorption in superconducting aluminum have been made in the wavelength region 20 mm to 3 mm. The results, when plotted as isotherms of surface resistance ratio vs photon energy, show that, at a well-defined energy for each temperature, there is a rapid rise in absorption with increasing energy. This has been interpreted as the onset of absorption resulting from direct excitation of electrons across a forbidden energy gap. The isotherms then permit the determination of the temperature dependence of this energy gap. At absolute zero the gap value is found to be ${\mathcal{E}}_g\mathrm{}\left(0\right)=(3.2\mathrm{}\pm 0.1)k{T}_c$ (where $T_c=1.178\mathrm{}°$K is the superconducting transition temperature), in reasonable agreement with the theoretical value of $3.52k{T}_c$ obtained by Bardeen, Cooper, and Schrieffer. Furthermore, the temperature variation of the gap exhibits the same shape as that given by the theory. Finally, reasonable agreement is obtained between theory and experiment concerning the detailed shapes of the surface resistance vs temperature curves over the measured wavelength range, provided that the experimental value ${\mathcal{E}}_g\mathrm{}\left(0\right)\mathrm{}$ is used in the theory.